There have apparently been ice caps on and off throughout the ages. They’re around for a while, then they go away. Most of the time there probably aren’t any, really, so they’re something of a novelty in that respect. And sometimes there is land at the poles, and sometimes just water (or ice). I think that the South Pole has been on Antarctica for at least the past 80 million years. I’m not sure how long the North Pole has been water.
There are almost certainly many reasons for the creation of the ice caps, not just one or two. The rise of the Tibetan Plateau almost certainly had a great impact on global climate, as LaMa said. And the movement of the continents and ocean currents probably did things to the movement of cold and warm water towards the North and South Poles. Then there are possible contributions from changes in the atmosphere.
As for what would happen if the ice caps melted. . .well, that’s going to call for a bit of speculation, especially as it partly depends on just what causes them to melt. Obviously, global warming through atmospheric build-up of carbon dioxide would have different results than, say, the Earth plunging into the Sun.
If it’s a nice peaceful melting from a gradual warming of the planet’s overall climate, then the sea levels are certain to rise. How much, I don’t know. I do know that there is evidence in some places of sea levels being something like 60 meters higher than now (I remember that number from reading the reports of cave excavations at Gibraltar). If that does happen, then it will change the outlines of the continents a lot. Not quite on the level movies like Waterworld would have you believe, but still quite a bit. Our friend LaMa in the Netherlands would need to be sure he could swim well, for one thing. And perhaps we’d end up with the American Great Plains being a sea again. I suppose you could get a topographical map of the world with elevations marked on it, and then start colouring in with blue all the sections open to the ocean that are below certain elevations to see what would stay and what would go.
Also, all that water melting would probably change the salinity levels of the ocean. That would have effects on all sorts of things, from the water temperatures to what sorts of creatures lived in it.
Some things might change in other ways as well. The weight of all that ice has pushed down places like Antarctica and Greenland. Maybe with all that extra weight gone, they will rise back up again?
Whatever happens, we’re no doubt in for some changes over the next few thousand years.